Nonhomogeneous Markov chain switching model

The paper is dedicated to a new approach to analyze changes of qualitative characteristic of economic process by means of a special kind of nonhomogeneous Markov chain basing on the concept of switching models. Qualitative feature of economic process (such as evaluation of economic situation) may be in natural way modeled by polynomial distribution. In the paper the authoress assumes that its distribution is a mixture of multinomial probability distributions with parameters dependent on transition probabilities of a Markov chain. Such approach let treat the data observed as an outcome of a nonhomogeneous Markov chain with transition matrix in each period belonging to a finite set of possible matrices. The choice of the matrix describing the process in each moment of observation is governed by an unobserved regime variable. In other words nonhomogeneity of a Markov chain consists in switches from one regime transition matrix to another. In the paper she develops maximum likelihood estimators of the model's parameters and presents the application of the model to analysis the responses from business tendency survey in Poland for the case of micro data (i.e. when the whole history of responses of each individual respondent is available) and macro data (only the structures of responses are available).